Some results on variational inequalities and generalized equilibrium problems with applications

Abstract

Abstract. An iterative algorithm is considered for variational inequalities, generalized equilibrium problems and fixed point problems. Strong convergence of the proposed iterative algorithm is obtained in the framework Hilbert spaces.Mathematical subject classification: 47H05, 47H09, 47J25, 47N10.

Iterative Algorithms for Mixed Equilibrium Problems, System of Quasi-Variational Inclusion, and Fixed Point Problem in Hilbert Spaces

“…Then, we prove strong convergence theorems which are connected with [5,[26][27][28][29]. Our results extend and improve the corresponding results of Jitpeera and Kumam [25], Liou [23], Plubtieng and Punpaeng [20], Petrot et al [24], Peng and Yao [21], Qin et al [22], and some authors.…”

“…In 2010, Qin et al [22] introduced an iterative method for finding solutions of a generalized equilibrium problem, the set of fixed points of a family of nonexpansive mappings, and the common variational inclusions. The sequences generated by 1 ∈ and { } are a sequence generated by…”

“…for all ∈ N ∪ {0}, where { }, { }, { } are three sequences in [0, 1] and ∈ (0, 2 ]. They proved that { } generated by (22) converges strongly to 0 which is the unique solution in ( ) ∩ ( , ).…”